Welcome to Android Central! The Internet browser is still functional? I ask this because if it somehow got disabled, that would also remove it from the sync list. If you can't even find the Internet browser to open, then go to the App Manager and look for a list of Disabled apps. If you find Internet there, tap it and Enable it.

Make sure they didn't somehow change the name from Internet to Browser (or something similar).

Indeed, the stock browser is fully functional, except for the lack of a "email.address(at)gmail.com" section in bookmarks (only "my device" is visible) and the missing "sync Internet" mentioned above. Mind, the Note II has been (Android\settings\accounts\backup and reset\) factory reset and automatically restored.

It's interesting--I was under the impression that the stock Internet browser on Samsung devices actually did not sync with your Chrome bookmarks. Are you saying that yours definitely did before the reset?

If "sync Internet" in Android\accounts\Google\... also syncs Chrome's bookmarks, I suppose so. In my experience, it is a basic Android faculty for syncing stock browser bookmarks. At least on my own Samsung S2 -- and Note II, until recently. An additional peculiarity, since the latter's reset, it's that it now has a Samsung bookmark which can't be deleted, edited or moved.

The problem seems to relate to a missing apk called com.google.android.syncadapters.bookmarks, which when installed re-adds the missing "sync Internet" feature. The post cited below links to a copy. While the original package is Google code, it requires many permissions beyond what seems necessary and the source of the copy is not transparent. TREAT WITH CARE.

Internet does not sync to your Gmail account, it syncs to your Samsung account if you have one or remember it.
Your Samsung account may have a Gmail address, like mine, but a Samsung logo.

Basic Google accounts provide "sync Internet" as well, when the necessary apk is present. Why it went missing after a factory reset, or a Samsung portal bookmark is now un-deletable, un-editable and immovable, I don't know - perhaps Samsung has rolled out new settings.

Basic Google accounts provide "sync Internet" as well, when the necessary apk is present. Why it went missing after a factory reset, or a Samsung portal bookmark is now un-deletable, un-editable and immovable, I don't know - perhaps Samsung has rolled out new settings.

Well - you got me there. I just have Chrome in my Google account and have no desire to add Internet there.
I always use Internet and have my pc IE bookmarks on it.

Installing the apk seems to have the intended effect. What caused the issue in the first place remains unclear. I agree that it's probably the result of intentional alterations in the Android setup script - rather than some error. The fact the pre-installed, localized Samsung portal bookmark is locked now, unlike the rest, makes me think it's Samsung, not Google.
Another, untested possibility is that on prior occasions I did not add WiFi details until after Android installation completed. This might have forced the setup procedure to use local, either outdated or generic setup scripts which install the now missing apk.

As far as I am concerned, the issue is now resolved. Thank you - both - for thinking along.